Powering the LEDs from the r/x is fine, providing it can output the necessary voltage and current; most servos give out 6V, so you could run two 3V LEDs in series (without resistors) - they only require 20-40 mA to function, easily supplied via the r/x - you could even connect several to the 6V output, in parallel (with resistors), depending on the current consumption. Even incandescent g-o-w/g-o-r bulbs could be used, although the current consumption is higher (100-200mA) - as you say, a servo consumes a lot of current to move.
A.